Paper: arXiv 2609.08541

Authors: Yingli Wang, Xiaoyu Wang

Abstract

We study variance-optimal stock hedging and the convergence of approximate strategies in the rough Hawkes–Heston model. Starting from the model’s affine conditional transform and the affine Volterra jump framework, we obtain semi-explicit hedges for European calls and a representation of the minimum quadratic error through the Galtchouk–Kunita–Watanabe projection. Our main approximation result keeps the original stock, variance driver, and information flow fixed while regularizing the kernel used to evaluate the hedge. To handle singular memory and common marked jumps, we construct the approximate holdings from histories available before trading and preserve the conditional transform’s random modulus envelope. Riccati–Volterra stability and weighted truncation then yield convergence in the original stock’s trading norm on compact Fourier intervals. For calls, a joint choice of kernel regularization and Fourier cutoff gives convergence of the initial capitals and strategies, uniform-in-time square-mean convergence of continuous-time gains, and convergence of the terminal mean-square error to the variance-optimal value. A numerical experiment with shifted fractional kernels illustrates the construction on common original-market paths.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly complex mathematical framework for hedging in a novel rough Hawkes-Heston model, demonstrating strong theoretical rigor. While the empirical section is limited to a numerical experiment, it effectively illustrates the theoretical construction and convergence properties, suggesting a path for future empirical validation. The combination of advanced mathematics and a clear path to practical application places it in the ‘Holy Grail’ quadrant.

Research Flowchart

  flowchart TD
    A[Research Goal: Variance-Optimal Hedging in Rough Hawkes-Heston] --> B{Methodology: Affine Volterra Jump & GKW Projection};
    B --> C[Data/Inputs: Model Parameters, Option Payoffs (European Calls)];
    C --> D{Computational Process: Kernel Regularization, Riccati-Volterra Stability, Weighted Truncation};
    D --> E[Key Outcomes: Semi-Explicit Hedges, Minimum Quadratic Error, Convergence Proofs, Numerical Illustration];

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